Question: Solve for $x$ and $y$ by deriving an expression for $y$ from the second equation, and substituting it back into the first equation. $\begin{align*}2x+7y &= 9 \\ 9x+4y &= -9\end{align*}$
Explanation: Begin by moving the $x$ -term in the second equation to the right side of the equation. $4y = -9x-9$ Divide both sides by $4$ to isolate $y$ $y = {-\dfrac{9}{4}x - \dfrac{9}{4}}$ Substitute this expression for $y$ in the first equation. $2x+7({-\dfrac{9}{4}x - \dfrac{9}{4}}) = 9$ $2x - \dfrac{63}{4}x - \dfrac{63}{4} = 9$ Simplify by combining terms, then solve for $x$ $-\dfrac{55}{4}x - \dfrac{63}{4} = 9$ $-\dfrac{55}{4}x = \dfrac{99}{4}$ $x = -\dfrac{9}{5}$ Substitute $-\dfrac{9}{5}$ for $x$ back into the top equation. $2( -\dfrac{9}{5})+7y = 9$ $-\dfrac{18}{5}+7y = 9$ $7y = \dfrac{63}{5}$ $y = \dfrac{9}{5}$ The solution is $\enspace x = -\dfrac{9}{5}, \enspace y = \dfrac{9}{5}$.